Robustness and generalization guarantees for statistical learning of generative models

We apply tools from the classical statistical learning theory to analyze theoretical properties of modern machine learning problems that are typically phrased in the context of generative models. By combining standard methods based on the theory of empirical processes with ideas from optimal transport and signal recovery, we formally address the generalization and robustness guarantees for the existing and newly suggested algorithms. More specifically, we consider the following three problems: First, we tackle the problem of domain adaptation, where the training data and the test data are drawn from two distributions that are related but not identical. We devise an empirical risk minimization algorithm based on local worst-case risks, and provide generalization and excess risk guarantees of the learned hypothesis, that are robust to drifts in generative models. Second, we consider the learning of coding schemes, where the goal is to minimize the reconstruction risk of the original signal. It turns out that the task can be viewed as approximating the signal-generating distributions by pushforwards of arbitrary distributions via reconstruction maps. We provide learning guarantees based on the notions of optimal transport and classic statistical learning, using reconstruction errors as hypotheses. Third, we propose a framework of assessing representation learning algorithms by evaluating their estimation capabilities of the representation generating the signal. Using polyhedral estimates from the signal recovery literature, we investigate the provably near-optimal guarantees of the topic model.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2019

Author dc:creator

• Lee, Jaeho

Contributors dc:contributor

• Raginsky, Maxim
• Srikant, Rayadurgam
• Veeravalli, Venugopal
• Dokmanić, Ivan

• statistical learning
• minimax learning
• learning a coding scheme
• representation learning

Statement dc:rights

• Copyright 2019 Jaeho Lee

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/104957

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/104957